Question: Rewrite as a simplified fraction. ${0.8\overline{40} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 840.404...\\ 10x &= 8.404...\end{align*}}$ Subtracting the two equations, we have: ${990x = 832}$ ${x = \dfrac{832}{990}} $ ${x = \dfrac{416}{495}} $